Theorems · Definition · category theory

CategoryTheory.regularTopology.equivalence

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [inst_2 : F.PreservesEffectiveEpis] →
            [inst_3 : F.ReflectsEffectiveEpis] →
              [inst_4 : F.Full] →
                [inst_5 : F.Faithful] →
                  [inst_6 : CategoryTheory.Preregular D] →
                    [inst_7 : F.EffectivelyEnough] →
                      (A : Type u₃) →
                        [inst_8 : CategoryTheory.Category.{v₃, u₃} A] →
                          [∀ (X : Dᵒᵖ),
                                CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.StructuredArrow X F.op) A] →
                            CategoryTheory.Sheaf (CategoryTheory.regularTopology C) A ≌
                              CategoryTheory.Sheaf (CategoryTheory.regularTopology D) A

The equivalence from regular sheaves on C to regular sheaves on D, given a fully faithful functor F : C ⥤ D to a preregular category, which preserves and reflects effective epimorphisms and satisfies F.EffectivelyEnough.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesEffectiveEpisCategoryTheory.Functor.ReflectsEffectiveEpisCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.PreregularCategoryTheory.Functor.EffectivelyEnoughCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShape